The invention relates to interferometers for profiling a test surface, and particularly to an interferometric integration technique that avoids propagation of phase errors due to 2.pi. discontinuities occurring in small areas of the test surface to the other areas thereof.
By way of background, so-called phase-shifting interferometry techniques are utilized by optical interferometers to compute the phase of the interference pattern produced by shifting the optical path difference (OPD) between a reference surface and a surface being tested.
In phase-shifting interferometry, the phase distribution across the interferogram is measured "modulo 2.pi.". In other words, the measured phase distribution will contain 2.pi. discontinuities which can only be eliminated as long as the slope of the wavefront being measured is small enough that the phase difference is less than .pi. between adjacent pixels of the detector array. If the latter condition is met, the phase discontinuities can be removed by adding or subtracting 2.pi. to the measured phase so that the resulting phase difference between adjacent pixels is always less than .pi.. The phase difference referred to, which must be less than .pi. between adjacent detector pixels, includes phase errors caused by electronic noise. Electronic noise includes "computational noise" due to the limited number of binary bits used to make the phase calculations according to the phase-shifting interferometric techniques utilized. Numerous phase-shifting interferometry techniques and apparatus are known, for example, as described in U.S. Pat. No. 4,639,139 issued Jan. 27, 1987 by Wyant et al. entitled "Optical Profiler Using Improved Phase-Shifting Interferometry", incorporated herein by reference.
It frequently is desirable to be able to test a rough surface having portions so steep that the measured phase difference between adjacent pixels (including phase difference due to the effects of electronic computational noise) is greater than .pi.. In this case the 2.pi. ambiguities cannot be eliminated by simple addition or subtraction of 2.pi. to the "measured" phase. Conventional so-called "phase unwrapping techniques", wherein the values computed modulo 2.pi. are matched by adding or subtracting multiples of 2.pi. so as to make the "unwrapped" phase continuous, are not useable on such steep portions of the surface being profiled. The sequential nature of known phase unwrapping techniques has the consequence that if an error is introduced into the phase by misjudging the number of multiples of 2.pi. added or subtracted to the integrated phase, that error "propagates" to all subsequently integrated values of phase, and hence to the corresponding surface profile heights of the surface being tested. Thus, 2.pi. discontinuities exist in the integrated surface profile. (In some cases, other methods, such as the two-wavelength technique of U.S. Pat. No. 4,832,489 (Wyant et al.) or the sub-Nyquist method described in U.S. Pat. No. 4,791,584 (Greivenkamp, Jr.) can be used to eliminate 2.pi. discontinuities.) As a practical matter, the computed and displayed surface profile of a surface with steep portions generally is much less accurate than is desired.
There is an unmet need for a single-wavelength technique to prevent propagation of errors introduced at locations of 2.pi. discontinuities on a surface from being included in or "propagating to" all subsequent phase calculations for the remaining area of the surface.